Flag curvatures of the unit sphere in a Minkowski-Randers space

On a real vector space V , a Randers norm Fˆ is defined by Fˆ = ˆα+βˆ, where ˆα is a Euclidean norm and βˆ is a covector. We show that the unit sphere Σ in the Randers space (V, Fˆ) has positive flag curvature, if and only if |βˆ|αˆ < (5 − √ 17)/2 ≈ 0.43845, thus answering a problem proposed by Prof. Zhongmin Shen. Moreover, we prove that the flag curvature of Σ has a universal lower bound −4.